Wesley Crusher - Beverly's teenaged son, academically very average, coming onboard the Enterprise makes him want to join Starfleet and start to really work hard (he will never outshine the officers onboard).
Wesley really was a missed opportunity.
If Star Trek had wanted the tie the show into a teen and twenties demographic, then show Wesley as tied into the other teens on the ship. There was a scene in ten forward with Wesley interacting with other ships people his own age. And one episode Wesley had a semi-girlfriend. But most of the time I received the feeling that Wesley was estranged from his peer group. Teens like to identify with people on TV who are popular. Not a guy who only want to hang out with people in their thirties and sixties. You couldn't really identify with Wesley the way he was written.
Despite what TPTB at Star Trek might have thought, no one in their teens wanted to be Wesley.
Look at it this way, Enterprise's first season premiered when I was fourteen, all the geeks in my school could identify with Trip, he seemed somehow like he was in his mid-late teens, he was cool, laid back, played the harmonica and he was Mr. Popular aboard the ship.
Trip was everything Wesley wasn't. There was a "Kill Wesley" sediment among Star Trek fans. Fans are still crying about Trip being killed in the last episode.